TSTP Solution File: PUZ129+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : PUZ129+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:11:39 EDT 2022
% Result : Theorem 1.80s 1.99s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 27 ( 14 unt; 0 nHn; 26 RR)
% Number of literals : 50 ( 15 equ; 24 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-1 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ person(A)
| ~ property1(A,honest,pos)
| ~ property1(A,industrious,pos)
| property1(dollar_f1(A),healthy,pos) ),
file('PUZ129+2.p',unknown),
[] ).
cnf(2,axiom,
( ~ person(A)
| ~ property1(A,honest,pos)
| ~ property1(A,industrious,pos)
| A = dollar_f1(A) ),
file('PUZ129+2.p',unknown),
[] ).
cnf(3,plain,
( ~ person(A)
| ~ property1(A,honest,pos)
| ~ property1(A,industrious,pos)
| dollar_f1(A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[2])]),
[iquote('copy,2,flip.4')] ).
cnf(4,axiom,
( ~ grocer(A)
| ~ property1(B,healthy,pos)
| A != B ),
file('PUZ129+2.p',unknown),
[] ).
cnf(5,axiom,
( ~ grocer(A)
| ~ property1(A,industrious,pos)
| property1(dollar_f2(A),honest,pos) ),
file('PUZ129+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ grocer(A)
| ~ property1(A,industrious,pos)
| A = dollar_f2(A) ),
file('PUZ129+2.p',unknown),
[] ).
cnf(7,plain,
( ~ grocer(A)
| ~ property1(A,industrious,pos)
| dollar_f2(A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.3')] ).
cnf(8,axiom,
( ~ cyclist(A)
| property1(dollar_f3(A),industrious,pos) ),
file('PUZ129+2.p',unknown),
[] ).
cnf(9,axiom,
( ~ cyclist(A)
| A = dollar_f3(A) ),
file('PUZ129+2.p',unknown),
[] ).
cnf(10,plain,
( ~ cyclist(A)
| dollar_f3(A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.2')] ).
cnf(19,axiom,
( ~ cyclist(A)
| person(dollar_f6(A)) ),
file('PUZ129+2.p',unknown),
[] ).
cnf(20,axiom,
( ~ cyclist(A)
| A = dollar_f6(A) ),
file('PUZ129+2.p',unknown),
[] ).
cnf(21,plain,
( ~ cyclist(A)
| dollar_f6(A) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
[iquote('copy,20,flip.2')] ).
cnf(22,axiom,
A = A,
file('PUZ129+2.p',unknown),
[] ).
cnf(23,axiom,
grocer(dollar_c2),
file('PUZ129+2.p',unknown),
[] ).
cnf(24,axiom,
cyclist(dollar_c1),
file('PUZ129+2.p',unknown),
[] ).
cnf(26,axiom,
dollar_c2 = dollar_c1,
file('PUZ129+2.p',unknown),
[] ).
cnf(27,plain,
grocer(dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[23]),26]),
[iquote('back_demod,23,demod,26')] ).
cnf(29,plain,
dollar_f6(dollar_c1) = dollar_c1,
inference(hyper,[status(thm)],[24,21]),
[iquote('hyper,24,21')] ).
cnf(30,plain,
person(dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[24,19]),29]),
[iquote('hyper,24,19,demod,29')] ).
cnf(32,plain,
dollar_f3(dollar_c1) = dollar_c1,
inference(hyper,[status(thm)],[24,10]),
[iquote('hyper,24,10')] ).
cnf(33,plain,
property1(dollar_c1,industrious,pos),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[24,8]),32]),
[iquote('hyper,24,8,demod,32')] ).
cnf(37,plain,
dollar_f2(dollar_c1) = dollar_c1,
inference(hyper,[status(thm)],[33,7,27]),
[iquote('hyper,33,7,27')] ).
cnf(38,plain,
property1(dollar_c1,honest,pos),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[33,5,27]),37]),
[iquote('hyper,33,5,27,demod,37')] ).
cnf(40,plain,
dollar_f1(dollar_c1) = dollar_c1,
inference(hyper,[status(thm)],[38,3,30,33]),
[iquote('hyper,38,3,30,33')] ).
cnf(41,plain,
property1(dollar_c1,healthy,pos),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[38,1,30,33]),40]),
[iquote('hyper,38,1,30,33,demod,40')] ).
cnf(42,plain,
$false,
inference(hyper,[status(thm)],[41,4,27,22]),
[iquote('hyper,41,4,27,22')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ129+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 01:43:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.80/1.99 ----- Otter 3.3f, August 2004 -----
% 1.80/1.99 The process was started by sandbox2 on n004.cluster.edu,
% 1.80/1.99 Wed Jul 27 01:43:36 2022
% 1.80/1.99 The command was "./otter". The process ID is 24280.
% 1.80/1.99
% 1.80/1.99 set(prolog_style_variables).
% 1.80/1.99 set(auto).
% 1.80/1.99 dependent: set(auto1).
% 1.80/1.99 dependent: set(process_input).
% 1.80/1.99 dependent: clear(print_kept).
% 1.80/1.99 dependent: clear(print_new_demod).
% 1.80/1.99 dependent: clear(print_back_demod).
% 1.80/1.99 dependent: clear(print_back_sub).
% 1.80/1.99 dependent: set(control_memory).
% 1.80/1.99 dependent: assign(max_mem, 12000).
% 1.80/1.99 dependent: assign(pick_given_ratio, 4).
% 1.80/1.99 dependent: assign(stats_level, 1).
% 1.80/1.99 dependent: assign(max_seconds, 10800).
% 1.80/1.99 clear(print_given).
% 1.80/1.99
% 1.80/1.99 formula_list(usable).
% 1.80/1.99 all A (A=A).
% 1.80/1.99 -((all A (person(A)&property1(A,honest,pos)&property1(A,industrious,pos)-> (exists B (property1(B,healthy,pos)&A=B))))& (all C (grocer(C)-> -(exists D (property1(D,healthy,pos)&C=D))))& (all E (grocer(E)&property1(E,industrious,pos)-> (exists F (property1(F,honest,pos)&E=F))))& (all G (cyclist(G)-> (exists H (property1(H,industrious,pos)&G=H))))& (all I (cyclist(I)&property1(I,unhealthy,pos)-> (exists J (property1(J,dishonest,pos)&I=J))))& (all K (person(K)&property1(K,healthy,pos)-> -(exists L (property1(L,unhealthy,pos)&K=L))))& (all M (person(M)&property1(M,honest,pos)-> -(exists N (property1(N,dishonest,pos)&M=N))))& (all O (grocer(O)-> (exists P (person(P)&O=P))))& (all Q (cyclist(Q)-> (exists R (person(R)&Q=R))))-> (all S (grocer(S)-> -(exists T (cyclist(T)&S=T))))).
% 1.80/1.99 end_of_list.
% 1.80/1.99
% 1.80/1.99 -------> usable clausifies to:
% 1.80/1.99
% 1.80/1.99 list(usable).
% 1.80/1.99 0 [] A=A.
% 1.80/1.99 0 [] -person(A)| -property1(A,honest,pos)| -property1(A,industrious,pos)|property1($f1(A),healthy,pos).
% 1.80/1.99 0 [] -person(A)| -property1(A,honest,pos)| -property1(A,industrious,pos)|A=$f1(A).
% 1.80/1.99 0 [] -grocer(C)| -property1(D,healthy,pos)|C!=D.
% 1.80/1.99 0 [] -grocer(E)| -property1(E,industrious,pos)|property1($f2(E),honest,pos).
% 1.80/1.99 0 [] -grocer(E)| -property1(E,industrious,pos)|E=$f2(E).
% 1.80/1.99 0 [] -cyclist(G)|property1($f3(G),industrious,pos).
% 1.80/1.99 0 [] -cyclist(G)|G=$f3(G).
% 1.80/1.99 0 [] -cyclist(I)| -property1(I,unhealthy,pos)|property1($f4(I),dishonest,pos).
% 1.80/1.99 0 [] -cyclist(I)| -property1(I,unhealthy,pos)|I=$f4(I).
% 1.80/1.99 0 [] -person(K)| -property1(K,healthy,pos)| -property1(L,unhealthy,pos)|K!=L.
% 1.80/1.99 0 [] -person(M)| -property1(M,honest,pos)| -property1(N,dishonest,pos)|M!=N.
% 1.80/1.99 0 [] -grocer(O)|person($f5(O)).
% 1.80/1.99 0 [] -grocer(O)|O=$f5(O).
% 1.80/1.99 0 [] -cyclist(Q)|person($f6(Q)).
% 1.80/1.99 0 [] -cyclist(Q)|Q=$f6(Q).
% 1.80/1.99 0 [] grocer($c2).
% 1.80/1.99 0 [] cyclist($c1).
% 1.80/1.99 0 [] $c2=$c1.
% 1.80/1.99 end_of_list.
% 1.80/1.99
% 1.80/1.99 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.80/1.99
% 1.80/1.99 This is a Horn set with equality. The strategy will be
% 1.80/1.99 Knuth-Bendix and hyper_res, with positive clauses in
% 1.80/1.99 sos and nonpositive clauses in usable.
% 1.80/1.99
% 1.80/1.99 dependent: set(knuth_bendix).
% 1.80/1.99 dependent: set(anl_eq).
% 1.80/1.99 dependent: set(para_from).
% 1.80/1.99 dependent: set(para_into).
% 1.80/1.99 dependent: clear(para_from_right).
% 1.80/1.99 dependent: clear(para_into_right).
% 1.80/1.99 dependent: set(para_from_vars).
% 1.80/1.99 dependent: set(eq_units_both_ways).
% 1.80/1.99 dependent: set(dynamic_demod_all).
% 1.80/1.99 dependent: set(dynamic_demod).
% 1.80/1.99 dependent: set(order_eq).
% 1.80/1.99 dependent: set(back_demod).
% 1.80/1.99 dependent: set(lrpo).
% 1.80/1.99 dependent: set(hyper_res).
% 1.80/1.99 dependent: clear(order_hyper).
% 1.80/1.99
% 1.80/1.99 ------------> process usable:
% 1.80/1.99 ** KEPT (pick-wt=15): 1 [] -person(A)| -property1(A,honest,pos)| -property1(A,industrious,pos)|property1($f1(A),healthy,pos).
% 1.80/1.99 ** KEPT (pick-wt=14): 3 [copy,2,flip.4] -person(A)| -property1(A,honest,pos)| -property1(A,industrious,pos)|$f1(A)=A.
% 1.80/1.99 ** KEPT (pick-wt=9): 4 [] -grocer(A)| -property1(B,healthy,pos)|A!=B.
% 1.80/1.99 ** KEPT (pick-wt=11): 5 [] -grocer(A)| -property1(A,industrious,pos)|property1($f2(A),honest,pos).
% 1.80/1.99 ** KEPT (pick-wt=10): 7 [copy,6,flip.3] -grocer(A)| -property1(A,industrious,pos)|$f2(A)=A.
% 1.80/1.99 ** KEPT (pick-wt=7): 8 [] -cyclist(A)|property1($f3(A),industrious,pos).
% 1.80/1.99 ** KEPT (pick-wt=6): 10 [copy,9,flip.2] -cyclist(A)|$f3(A)=A.
% 1.80/1.99 ** KEPT (pick-wt=11): 11 [] -cyclist(A)| -property1(A,unhealthy,pos)|property1($f4(A),dishonest,pos).
% 1.80/1.99 ** KEPT (pick-wt=10): 13 [copy,12,flip.3] -cyclist(A)| -property1(A,unhealthy,pos)|$f4(A)=A.
% 1.80/1.99 ** KEPT (pick-wt=13): 14 [] -person(A)| -property1(A,healthy,pos)| -property1(B,unhealthy,pos)|A!=B.
% 1.80/1.99 ** KEPT (pick-wt=13): 15 [] -person(A)| -property1(A,honest,pos)| -property1(B,dishonest,pos)|A!=B.
% 1.80/1.99 ** KEPT (pick-wt=5): 16 [] -grocer(A)|person($f5(A)).
% 1.80/1.99 ** KEPT (pick-wt=6): 18 [copy,17,flip.2] -grocer(A)|$f5(A)=A.
% 1.80/1.99 ** KEPT (pick-wt=5): 19 [] -cyclist(A)|person($f6(A)).
% 1.80/1.99 ** KEPT (pick-wt=6): 21 [copy,20,flip.2] -cyclist(A)|$f6(A)=A.
% 1.80/1.99
% 1.80/1.99 ------------> process sos:
% 1.80/1.99 ** KEPT (pick-wt=3): 22 [] A=A.
% 1.80/1.99 ** KEPT (pick-wt=2): 23 [] grocer($c2).
% 1.80/1.99 ** KEPT (pick-wt=2): 24 [] cyclist($c1).
% 1.80/1.99 ** KEPT (pick-wt=3): 25 [] $c2=$c1.
% 1.80/1.99 ---> New Demodulator: 26 [new_demod,25] $c2=$c1.
% 1.80/1.99 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] A=A.
% 1.80/1.99 >>>> Starting back demodulation with 26.
% 1.80/1.99 >> back demodulating 23 with 26.
% 1.80/1.99
% 1.80/1.99 ======= end of input processing =======
% 1.80/1.99
% 1.80/1.99 =========== start of search ===========
% 1.80/1.99
% 1.80/1.99 -------- PROOF --------
% 1.80/1.99
% 1.80/1.99 -----> EMPTY CLAUSE at 0.00 sec ----> 42 [hyper,41,4,27,22] $F.
% 1.80/1.99
% 1.80/1.99 Length of proof is 13. Level of proof is 7.
% 1.80/1.99
% 1.80/1.99 ---------------- PROOF ----------------
% 1.80/1.99 % SZS status Theorem
% 1.80/1.99 % SZS output start Refutation
% See solution above
% 1.80/1.99 ------------ end of proof -------------
% 1.80/1.99
% 1.80/1.99
% 1.80/1.99 Search stopped by max_proofs option.
% 1.80/1.99
% 1.80/1.99
% 1.80/1.99 Search stopped by max_proofs option.
% 1.80/1.99
% 1.80/1.99 ============ end of search ============
% 1.80/1.99
% 1.80/1.99 -------------- statistics -------------
% 1.80/1.99 clauses given 13
% 1.80/1.99 clauses generated 38
% 1.80/1.99 clauses kept 29
% 1.80/1.99 clauses forward subsumed 29
% 1.80/1.99 clauses back subsumed 0
% 1.80/1.99 Kbytes malloced 976
% 1.80/1.99
% 1.80/1.99 ----------- times (seconds) -----------
% 1.80/1.99 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/1.99 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/1.99 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.80/1.99
% 1.80/1.99 That finishes the proof of the theorem.
% 1.80/1.99
% 1.80/1.99 Process 24280 finished Wed Jul 27 01:43:38 2022
% 1.80/1.99 Otter interrupted
% 1.80/1.99 PROOF FOUND
%------------------------------------------------------------------------------